Reply to "Comment on "Chiral symmetry restoration, the eigenvalue density of the Dirac operator, and the axial U(1) anomaly at finite temperature""

Abstract

We respond to the comment by Matteo Giordano [1] on our article [2]. We find -- and [1] itself acknowledges -- that the proposed counterexamples intended to refute our argument violate a crucial assumption of QCD at high temperatures, namely that every gluonic observable is an analytic function of the squared quark mass, $m^2$. We further point out a technical mistake found in [1]. We conclude that the arguments presented in [1] are not valid.

Comments: 5 pages, to appear in PRD(Reply), reply to arXiv:2510.24403